Maybe this time he’ll play it straight and actually play into our expectations? The swerve could be that there IS NO swerve! It’s like M. Night Shama-whatever, except with a guy that does WAY better storytelling!

I have actively ignored the sock gap just to prove that’s not true. However, the downside is that EVERY TIME I have sex now, I think about Jeff. I am doomed to an eternity of picturing that curly-haired bag of neurosis every time I’m makin’ it with a woman. That’s… goddammit…

Think of it like Piccolo and Gohan’s weighted shoulderpads. He’s been “fighting” this whole time with a handicap.

He’s finally gotten to the point where he feels it necessary to dramatically toss the weighted duds aside with a mighty thud, prior to spending the next three minutes showing her what he’s capable of when he’s “done warming up”.

(If you couldn’t guess, I’m implying that he’s going to break into a Gilbert and Sullivan patter routine.)

C’mon, Jason, it’s been twenty years since Calculus for me, and I could still give a less circular explanation of dx than that. You’re deliberately tormenting Sal by keeping her here with lousy tutoring until she succumbs to nicotine withdrawal and sexual frustration, aren’t you?

(I just realized that I took Calc before DoA Sal was born. Holy Cheese, I’m old.)

I’d be interested in seeing a less circular definition. MY problem with whatever definition he was going to give was that it seems like its not right. dx is not a derivative. Its a differential. dx is really just another variable.
d(y(x)) = y'(x)*dx. So dy is a function of two variables: x and dx. (Note that if y = x we have d(x) = 1 * dx = dx . Also, dy/dx = (y'(x) * dx)/dx = y'(x) )

It suddenly occurs to me that if only these tutoring sessions were shown in more detail, then this could be part of a secret plot to improve mathematical literacy in webcomic readers.

By the way, it appears that my poor Billie/Sal ship is now under fire from both sides. Port and starboard sides. Port being an alcoholic beverage, and consequently Billie. I have no humorous explanation for why Sal is the starboard side.

She isn’t really asking the right question either or Jason isn’t explaining it right. With Math it’s not about what this is, it’s about what it does and how it works. You can explain theory all day but without any practical examples you’re not gonna get anywhere. At least that’s how it was with me. Practice it a few times and THEN the theory started making sense.

Great amusement at her reaction to {his transition from panel one to panel five}, as well as at the transition itself.

—

(*mostly to self*) dx is an infinitesimal change in x, df(x) likewise for f(x), and df(x)/dx is effectively the slope of f(x). That much I remember. What I don’t remember, disturbingly, is why you subtract one from an x’s exponent and multiply its coefficient by its former exponent. C and x, yes, but x^2 or higher… hrm.

I now want to search that down and learn it intuitively again. By contrast, I remember enough about integration to recall that carrying it out usually involved a torturous toolbox of tricks for rearranging expressions into something that could be integrated. So that field I won’t be revisiting until I find a way to artificially augment my cognitive abilities substantially.

The derivative of x^2 is 2x, and that checks out with the negatives of the parabola, but /why/…

Oh gods. When trying to relearn this, inadvertently slammed into references to the product rule and the chain rule. Skin crawling to a startling degree, given how much I enjoyed maths in theory. Going and doing something completely utterly unrelated now. Curiosity being the problem.

df(x)/dx = f'(x), then there’s df'(x)/dx = f”(x), the slope of f'(x)… no problem there, but why… why is 2x the slope of x^2…!? I was actually taught that, yes? I wasn’t just taught what to do with the numbers without being told why!?

Newton’s quotient. f'(x) = the limit of [f(x+h) – f(x)]/h as h -> 0. h can be delta-x, or dx, if you prefer. For finite h the formula is the slope of a secant line connecting two points of the curve; as h goes to 0 it becomes the tangent line, the slope at a single point.

Plug in a polynomial like f(x)=x^2 and you should get 2x, if your algebra hasn’t atrophied. Trig derivatives are trickier, it’s easy to set up but you have to do some clever geometry to see that the limit of sin(h)/h is cos(h).

Belatedly noticed: dy/dx is the derivative of y with respect to x. ‘dx’ alone is not in fact a derivative of anything. If Jason is in fact trying to explain dx as as though it’s a derivative of something in itself (rather than a limit delta), this may somewhat explain why someone he’s teaching directly is having so much trouble.

Hoo boy, I feel that pain. I’ve been in Sal’s position of trying to force my brain around a concept that it refuses to understand and fully realizes it has no use for. My brain likes to put up blocks when it catches on that it’ll never see or use this information again outside the class.

dx is not a derivative, it’s a differential (an infinitesimally small increment of the variable x). A derivative would be dy/dx (the derivative of y with respect to x) or, in a different notation, Dy. No wonder Sal doesn’t understand.

Never ask a TA a question like that. Pretty consistently they are clueless about the abstract concepts behind the subject and are only good for rote learning or working over specific problems. the place to go for a question like that is the actual professor in his office hours or hire a tutor who actually understands the comcepts and can explain them to a newbie.

Eh, generally math TAs should have a solid grap on elementary calculus and quite a lot more, otherwise they wouldn’t be awarded the position. It is true however, that young TAs often aren’t that good at teaching students, since often they were at the very top of their college class.

*Snork*! Sorry, I couldn’t help it. You just described the ideal. The reality is that a large portion of TAs are just recent grad students trying to get through their Master’s with a minimum of distraction. There are also a lot of people who do Calculus very well without really understanding it completely. Those people, who make up a major part of the TA community, are great for questions about specific problems and algorithms, but when you ask them something like “what is dx, really”, they can’t go beyond their “talking points” and just spit out the same thing over and over because they can’t afford to admit that they don’t really know. It’s not entirely their fault; the acid test of really understanding a concept is the be able to explain it to people who is starting from scratch. I don’t mean that they don’t have a basic background in Trig or Algebra, but newbies from a Calculus perspective. Concepts like dy and dx are very abstract and hard to pin down (actually Newton was pretty disdainful of them and preferred the simple “f'(x)” notation) and very frustrating when the person explaining them to you tends to take you on a circular primrose path.

Of course, the college also has a lot to do with it. One could probably more reasonably expect a TA from MIT to be up to the task than one from IU.